






import importlib
import os
import sys


# This is required to make the module import works (when the python process is running from the root of the repo)
sys.path.append(".")




def 				A		(					lowercase__  :  List[str]  )		-> Tuple:
	UpperCamelCase__ :Dict						=      test_file.split(os.path.sep  )
	if components[0:2] != ["tests", "models"]:
		raise ValueError(
		    """`test_file` should start with `tests/models/` (with `/` being the OS specific path separator). Got """
		    f"""{test_file} instead."""  )
	UpperCamelCase__ :Optional[int]						=      components[-1]
	if not test_fn.endswith("""py"""  ):
		raise ValueError(f"""`test_file` should be a python file. Got {test_fn} instead."""  )
	if not test_fn.startswith("""test_modeling_"""  ):
		raise ValueError(
		    f"""`test_file` should point to a file name of the form `test_modeling_*.py`. Got {test_fn} instead."""  )

	UpperCamelCase__ :Union[str, Any]						=      components[:-1] + [test_fn.replace(""".py""" ,		""""""  )]
	UpperCamelCase__ :List[Any]						=      """.""".join(lowercase__  )

	return test_module_path




def 				A		(					lowercase__  :  int  )		-> Tuple:
	UpperCamelCase__ :Optional[Any]						=      get_module_path(lowercase__  )
	UpperCamelCase__ :List[str]						=      importlib.import_module(lowercase__  )

	return test_module




def 				A		(					lowercase__  :  Union[str, Any]  )		-> int:
	UpperCamelCase__ :Optional[int]						=      []
	UpperCamelCase__ :str						=      get_test_module(lowercase__  )
	for attr in dir(lowercase__  ):
		if attr.endswith("""ModelTester"""  ):
			tester_classes.append(getattr(lowercase__ ,		lowercase__  )  )

    # sort with class names
	return sorted(lowercase__ ,		key=lambda lowercase__  : x.__name__  )




def 				A		(					lowercase__  :  Union[str, Any]  )		-> Optional[Any]:
	UpperCamelCase__ :int						=      []
	UpperCamelCase__ :Union[str, Any]						=      get_test_module(lowercase__  )
	for attr in dir(lowercase__  ):
		UpperCamelCase__ :Optional[int]						=      getattr(lowercase__ ,		lowercase__  )
		# (TF/Flax)ModelTesterMixin is also an attribute in specific model test module. Let's exclude them by checking
		# `all_model_classes` is not empty (which also excludes other special classes).
		UpperCamelCase__ :Union[str, Any]						=      getattr(lowercase__ ,		"""all_model_classes""" ,		[]  )
		if len(lowercase__  ) > 0:
			test_classes.append(lowercase__  )

    # sort with class names
	return sorted(lowercase__ ,		key=lambda lowercase__  : x.__name__  )




def 				A		(					lowercase__  :  Dict  )		-> Union[str, Any]:
	UpperCamelCase__ :List[str]						=      get_test_classes(lowercase__  )
	UpperCamelCase__ :Optional[Any]						=      set()
	for test_class in test_classes:
		model_classes.update(test_class.all_model_classes  )

	# sort with class names
	return sorted(lowercase__ ,		key=lambda lowercase__  : x.__name__  )




def 				A		(					lowercase__  :  List[str]  )		-> List[str]:
	UpperCamelCase__ :Any						=      test_class()
	if hasattr(lowercase__ ,		"""setUp"""  ):
		test.setUp()

	UpperCamelCase__ :str						=      None
	if hasattr(lowercase__ ,		"""model_tester"""  ):
		# `(TF/Flax)ModelTesterMixin` has this attribute default to `None`. Let's skip this case.
		if test.model_tester is not None:
			UpperCamelCase__ :str						=      test.model_tester.__class__

	return model_tester




def 				A		(					lowercase__  :  List[Any] ,		lowercase__  :  Optional[Any]  )		-> Optional[int]:
	UpperCamelCase__ :int						=      get_test_classes(lowercase__  )

	UpperCamelCase__ :str						=      []
	for test_class in test_classes:
		if model_class in test_class.all_model_classes:
			target_test_classes.append(lowercase__  )

    # sort with class names
	return sorted(lowercase__ ,		key=lambda lowercase__  : x.__name__  )




def 				A		(					lowercase__  :  Tuple ,		lowercase__  :  Optional[int]  )		-> List[Any]:
	UpperCamelCase__ :Optional[Any]						=      get_test_classes_for_model(lowercase__ ,		lowercase__  )

	UpperCamelCase__ :Optional[Any]						=      []
	for test_class in test_classes:
		UpperCamelCase__ :Optional[int]						=      get_model_tester_from_test_class(lowercase__  )
		if tester_class is not None:
			tester_classes.append(lowercase__  )

    # sort with class names
	return sorted(lowercase__ ,		key=lambda lowercase__  : x.__name__  )




def 				A		(					lowercase__  :  Tuple  )		-> Optional[Any]:
	UpperCamelCase__ :Tuple						=      get_test_classes(lowercase__  )
	UpperCamelCase__ :Any						=      {test_class: get_model_tester_from_test_class(lowercase__  ) for test_class in test_classes}
	return test_tester_mapping




def 				A		(					lowercase__  :  int  )		-> Tuple:
	UpperCamelCase__ :Tuple						=      get_model_classes(lowercase__  )
	UpperCamelCase__ :Dict						=      {
	    model_class: get_test_classes_for_model(lowercase__ ,		lowercase__  ) for model_class in model_classes
	}
	return model_test_mapping




def 				A		(					lowercase__  :  str  )		-> Union[str, Any]:
	UpperCamelCase__ :Optional[int]						=      get_model_classes(lowercase__  )
	UpperCamelCase__ :Tuple						=      {
	    model_class: get_tester_classes_for_model(lowercase__ ,		lowercase__  ) for model_class in model_classes
	}
	return model_to_tester_mapping




def 				A		(					lowercase__  :  Optional[Any]  )		-> List[str]:
	if isinstance(lowercase__ ,		lowercase__  ):
		return o
	elif isinstance(lowercase__ ,		lowercase__  ):
		return o.__name__
	elif isinstance(lowercase__ ,		(list, tuple)  ):
		return [to_json(lowercase__  ) for x in o]
	elif isinstance(lowercase__ ,		lowercase__  ):
		return {to_json(lowercase__  ): to_json(lowercase__  ) for k, v in o.items()}
	else:
		return o




'''simple docstring'''



from collections import defaultdict
def        UpperCAmelCase (    A	:					int					):
							SCREAMING_SNAKE_CASE       :   List[Any]         =      1
							SCREAMING_SNAKE_CASE       :   Dict         =      True
							for v in tree[start]:
														if v not in visited:
																					ret += dfs(A					)
							if ret % 2 == 0:
														cuts.append(A					)
							return ret
def        UpperCAmelCase (    ):
							dfs(1					)


if __name__ == "__main__":
							lowerCAmelCase_      ,				lowerCAmelCase_  :							Dict             =    10, 9
							lowerCAmelCase_  :							Dict             =    defaultdict(list)
							lowerCAmelCase_  :							dict[int, bool]             =    {}
							lowerCAmelCase_  :							list[int]             =    []
							lowerCAmelCase_  :							Optional[Any]             =    0
							lowerCAmelCase_  :							Dict             =    [(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
							for u, v in edges:
														tree[u].append(v)
														tree[v].append(u)
							even_tree()
							print(len(cuts) - 1)




